The set of answer sets of a logic program \(\Pi \)  is denoted by \(\mathit {AS}(\Pi )\) .
The consistency problem of ASP, that is, to decide whether for a given
logic program \(\Pi \)  it holds that \(\mathit {AS}(\Pi )\ne \emptyset \) , is
\(\Sigma _{\mathit {P}}^{\mathit {2}}\) -complete [1]}, and remains so also in the case
where doubly negated atoms are allowed in rule bodies [2]}.
